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There are two 18-tuples of 71 integers. Namely {71; 0, 0, 4, 0} and {71; 0, 0, 3, 2}.
The 18-tuples are integers from x+1 to x+71, where x satisfies the following equations.

First case of {71; 0, 0, 4, 0} :
x = 2*n2 + 0
x = 3*n3 + 0
x = 5*n5 + 4
x = 7*n7 + 0

This 18-tuple resides in the integers
x+1, x+2, x+3, x+5, ... x+69, x+70, x+71

x = 2*n2 + 0 annihilates x+2, x+4,  x+6, ...   x+68, x+70
x = 3*n3 + 0 annihilates x+3, x+6,  x+9, ...  x+66, x+69
x = 5*n5 + 4 annihilates x+4, x+9,  x+14, ... x+64, x+69
x = 7*n7 + 0 annihilates x+7, x+14, x+21, ... x+63, x+70

This creates the admissible 18-tuple of

x+1,  x+5,  x+11, x+13, x+17, x+23, x+25, x+31, x+37, x+41,
x+43, x+47, x+53, x+55, x+61, x+65, x+67,  and  x+71

which by the Chinese Remainder Theorem is equivalent to

x = 210 * n + 84

===============================================================

Second case of {71; 0, 0, 3, 2} :
x = 2*n2 + 0
x = 3*n3 + 0
x = 5*n5 + 3
x = 7*n7 + 2

x = 210 * n + 198

(the inverse of the first tuple)

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Note: There are tuples that are symmetrical.
The symmetrical tuples are :

2-tuple of x+1, x+3
2-tuple of x+1, x+5
4-tuple of x+1, x+3, x+7, x+9
4-tuple of x+1, x+5, x+7, x+11
6-tuple of x+1, x+5, x+7, x+11, x+13, x+17
8-tuple of x+1, x+3, x+7, x+13, x+15, x+21, x+25, x+27
10-tuple of x+1, x+5, x+7, x+11, x+17, x+19, x+25, x+29, x+31, x+35
12-tuple of x+1, x+5, x+7, x+11, x+13, x+23, x+25, x+35, x+37, x+41, x+43, x+47

and my favorite is the
10-tuple of x+1, x+3, x+7, x+9,  x+19, x+21, x+31, x+33, x+37, x+39
which is symmetrical and consists of 5 prime pairs.
Graphically, it is
                        1 2         3 3   3 3
      1 2   7 9         9 1         1 3   7 9
      x.x...x.x.........x.x.........x.x...x.x

'x' represents admissible locations of primes